reply to Jurrian

Lajany x03002f at math.nagoya-u.ac.jp
Mon Jul 7 23:41:04 MDT 2003


Jurrian wrote:
>
> One day in the 1970s, I attended a public lecture at Christ's College,
> Christchurch, New Zealand, and a mathematician explained to me that you
> could devise a set of equations such that, at the end of the reasoning,
> zero = a non-zero number. I do not remember the details, but it made me
> a little skeptical about mathematics and number theory. After all, it is
> supposed to be that 0=0 and if you start to say 0=2 then you've got a
> problem.
>
There are commonly two ways to come up with expression like 0=2. The first
is to make an elementary arithmetic or algebraic error such as U.S.
undergraduate students usually make, thanks to the invidious race and
class discrimination built into the public school system there. The
second is to consider the ring of integers modulo 2. In the latter case,
the integers are divided into the class of odd integers (which are said to
be "equivalent to one mod two", and the class of even integers (which are
said to be "equivalent to zero mod two"). Addition in this system, is
carried out according to the rule that a+b=0 if a and b are both even or
both odd, and a+b=1 otherwise. This is a system where the statement
. . . -2=0=2=4=6=. . .  is perfectly legitimate and where "you don't have
a problem."
je




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